Which of the following functions has vertical asymptotes at $x=1$ and $x=3$ and horizontal asymptote $y=1$?

(a) $\displaystyle y=\frac{x}{(x-1)(x-3)}$

(b) $\displaystyle y=\frac{x^2}{(x-1)(x-3)}$

(c) $\displaystyle y=\frac{x^3}{(x-1)(x-3)}$